To understand the enhanced surface roughness for \(f^{ad}\)  beyond \(2 \times 10^{-4}\) , we focus on the displacement of individual particles located at the aggregate boundary. We noted previously that the dramatic variations in the particle dynamics between the core and periphery of the aggregate [1]}, [2]}, is a consequence of active processes being manifested predominantly on the surface of the aggregate. Consequently, we calculated the radial MSD (\(\Delta _r(t)\) ) and transverse MSD (\(\Delta _{\theta }(t)\) ) for particles whose distance from the aggregate center was greater than \(\Delta r(t=11\tau )/2\)  thus selecting for particles
at the boundary. We define the transverse MSD (\(\Delta _{\theta }(t)\) ) as,
\(\Delta _{\theta }(t-t_i, t_i)=\frac{1}{N}\sum _{k=1}^{k=N}[\delta {\bf r}^{\theta }_k(t-t_i, t_i)]^2,\) 
